pikascript/package/fuzzypid/fuzzy_PID.c

#include "fuzzy_PID.h"

struct fuzzy* fuzzy_init(unsigned int input_num, unsigned int output_num) {
    struct fuzzy* fuzzy_struct =
        (struct fuzzy*)pika_platform_malloc(sizeof(struct fuzzy));
    fuzzy_struct->input_num = input_num;
    fuzzy_struct->output_num = output_num;
    fuzzy_struct->mf_type = (unsigned int*)pika_platform_malloc(
        (input_num + output_num) * sizeof(unsigned int));
#ifdef fuzzy_pid_rule_base_deep_copy
    fuzzy_struct->mf_params =
        (int*)pika_platform_malloc(4 * qf_default * sizeof(int));
    fuzzy_struct->rule_base = (int*)pika_platform_malloc(
        output_num * qf_default * qf_default * sizeof(int));
#endif
    fuzzy_struct->output =
        (float*)pika_platform_malloc(output_num * sizeof(float));
    return fuzzy_struct;
}

void delete_fuzzy(struct fuzzy* fuzzy_struct) {
    pika_platform_free(fuzzy_struct->mf_type);
    pika_platform_free(fuzzy_struct->output);
    pika_platform_free(fuzzy_struct);
}

void fuzzy_params_init(struct fuzzy* fuzzy_struct,
                       unsigned int mf_type,
                       unsigned int fo_type,
                       unsigned int df_type,
                       int mf_params[],
                       int rule_base[][qf_default]) {
    for (unsigned int i = 0;
         i < fuzzy_struct->input_num + fuzzy_struct->output_num; ++i) {
        fuzzy_struct->mf_type[i] = mf_type;
    }

    for (unsigned int i = 0; i < fuzzy_struct->output_num; ++i) {
        fuzzy_struct->output[i] = 0;
    }

#ifdef fuzzy_pid_rule_base_deep_copy
    for (unsigned int j = 0; j < 4 * qf_default; ++j) {
        fuzzy_struct->mf_params[j] = mf_params[j];
    }

    for (unsigned int k = 0; k < fuzzy_struct->output_num * qf_default; ++k) {
        for (unsigned int i = 0; i < qf_default; ++i) {
            fuzzy_struct->rule_base[k * 7 + i] = rule_base[k][i];
        }
    }
#else
    fuzzy_struct->mf_params = mf_params;
    fuzzy_struct->rule_base = (int*)rule_base;
#endif

    fuzzy_struct->fo_type = fo_type;
    fuzzy_struct->df_type = df_type;
}

#define inverse(parameter) 1.0f / (float)parameter

// Gaussian membership function
float gaussmf(float x, float sigma, float c) {
    return expf(-powf(((x - c) / sigma), 2.0f));
}

// Generalized bell-shaped membership function
float gbellmf(float x, float a, float b, float c) {
    return inverse(1.0f + powf(fabsf((x - c) / a), 2.0f * b));
}

// Sigmoidal membership function
float sigmf(float x, float a, float c) {
    return inverse(1.0f + expf(a * (c - x)));
}

// Trapezoidal membership function
float trapmf(float x, float a, float b, float c, float d) {
    if (x >= a && x < b)
        return (x - a) / (b - a);
    else if (x >= b && x < c)
        return 1.0f;
    else if (x >= c && x <= d)
        return (d - x) / (d - c);
    else
        return 0.0f;
}

// Triangular membership function
float trimf(float x, float a, float b, float c) {
    return trapmf(x, a, b, b, c);
}

// Z-shaped membership function
float zmf(float x, float a, float b) {
    if (x <= a)
        return 1.0f;
    else if (x >= a && x <= (a + b) / 2.0f)
        return 1.0f - 2.0f * powf((x - a) / (b - a), 2.0f);
    else if (x >= (a + b) / 2.0f && x < b)
        return 2.0f * powf((x - b) / (b - a), 2.0f);
    else
        return 0;
}

// Membership function
float mf(float x, unsigned int mf_type, int* params) {
    switch (mf_type) {
        case 0:
            return gaussmf(x, params[0], params[1]);
        case 1:
            return gbellmf(x, params[0], params[1], params[2]);
        case 2:
            return sigmf(x, params[0], params[2]);
        case 3:
            return trapmf(x, params[0], params[1], params[2], params[3]);
        case 5:
            return zmf(x, params[0], params[1]);
        default:  // set triangular as default membership function
            return trimf(x, params[0], params[1], params[2]);
    }
}

// Union operator
float or (float a, float b, unsigned int type) {
    if (type == 1) {  // algebraic sum
        return a + b - a * b;
    } else if (type == 2) {  // bounded sum
        return fminf(1, a + b);
    } else {  // fuzzy union
        return fmaxf(a, b);
    }
}

// Intersection operator
float and (float a, float b, unsigned int type) {
    if (type == 1) {  // algebraic product
        return a * b;
    } else if (type == 2) {  // bounded product
        return fmaxf(0, a + b - 1);
    } else {  // fuzzy intersection
        return fminf(a, b);
    }
}

// Equilibrium operator
float equilibrium(float a, float b, float params) {
    return powf(a * b, 1 - params) * powf(1 - (1 - a) * (1 - b), params);
}

// Fuzzy operator
float fo(float a, float b, unsigned int type) {
    if (type < 3) {
        return and(a, b, type);
    } else if (type < 6) {
        return or (a, b, type - 3);
    } else {
        return equilibrium(a, b, 0.5f);
    }
}

// Mean of centers defuzzifier, only for two input multiple index
void moc(const float* joint_membership,
         const unsigned int* index,
         const unsigned int* count,
         struct fuzzy* fuzzy_struct) {
    float denominator_count = 0;
    float numerator_count[fuzzy_struct->output_num];
    for (unsigned int l = 0; l < fuzzy_struct->output_num; ++l) {
        numerator_count[l] = 0;
    }

    for (int i = 0; i < count[0]; ++i) {
        for (int j = 0; j < count[1]; ++j) {
            denominator_count += joint_membership[i * count[1] + j];
        }
    }

    for (unsigned int k = 0; k < fuzzy_struct->output_num; ++k) {
        for (unsigned int i = 0; i < count[0]; ++i) {
            for (unsigned int j = 0; j < count[1]; ++j) {
                numerator_count[k] +=
                    joint_membership[i * count[1] + j] *
                    fuzzy_struct->rule_base[k * qf_default * qf_default +
                                            index[i] * qf_default +
                                            index[count[0] + j]];
            }
        }
    }

#ifdef fuzzy_pid_debug_print
    pika_platform_printf("output:\n");
#endif
    for (unsigned int l = 0; l < fuzzy_struct->output_num; ++l) {
        fuzzy_struct->output[l] = numerator_count[l] / denominator_count;
#ifdef fuzzy_pid_debug_print
        pika_platform_printf("%f,%f,%f\n", numerator_count[l],
                             denominator_count, fuzzy_struct->index[l]);
#endif
    }
}

// Defuzzifier
void df(const float* joint_membership,
        const unsigned int* output,
        const unsigned int* count,
        struct fuzzy* fuzzy_struct,
        int df_type) {
    if (df_type == 0)
        moc(joint_membership, output, count, fuzzy_struct);
    else {
        pika_platform_printf("Waring: No such of defuzzifier!\n");
        moc(joint_membership, output, count, fuzzy_struct);
    }
}

void fuzzy_control(float e, float de, struct fuzzy* fuzzy_struct) {
    float membership[qf_default * 2];    // Store membership
    unsigned int index[qf_default * 2];  // Store the index of each membership
    unsigned int count[2] = {0, 0};

    {
        int j = 0;
        for (int i = 0; i < qf_default; ++i) {
            float temp = mf(e, fuzzy_struct->mf_type[0],
                            fuzzy_struct->mf_params + 4 * i);
            if (temp > 1e-4) {
                membership[j] = temp;
                index[j++] = i;
            }
        }

        count[0] = j;

        for (int i = 0; i < qf_default; ++i) {
            float temp = mf(de, fuzzy_struct->mf_type[1],
                            fuzzy_struct->mf_params + 4 * i);
            if (temp > 1e-4) {
                membership[j] = temp;
                index[j++] = i;
            }
        }

        count[1] = j - count[0];
    }

#ifdef fuzzy_pid_debug_print
    pika_platform_printf("membership:\n");
    for (unsigned int k = 0; k < j; ++k) {
        pika_platform_printf("%f\n", membership[k]);
    }

    pika_platform_printf("index:\n");
    for (unsigned int k = 0; k < j; ++k) {
        pika_platform_printf("%d\n", index[k]);
    }

    pika_platform_printf("count:\n");
    for (unsigned int k = 0; k < 2; ++k) {
        pika_platform_printf("%d\n", count[k]);
    }
#endif

    if (count[0] == 0 || count[1] == 0) {
        for (unsigned int l = 0; l < fuzzy_struct->output_num; ++l) {
            fuzzy_struct->output[l] = 0;
        }
        return;
    }

    // Joint membership
    float joint_membership[count[0] * count[1]];

    for (int i = 0; i < count[0]; ++i) {
        for (int j = 0; j < count[1]; ++j) {
            joint_membership[i * count[1] + j] = fo(
                membership[i], membership[count[0] + j], fuzzy_struct->fo_type);
        }
    }

    df(joint_membership, index, count, fuzzy_struct, 0);
}

struct PID* raw_fuzzy_pid_init(float kp,
                               float ki,
                               float kd,
                               float integral_limit,
                               float dead_zone,
                               float feed_forward,
                               float error_max,
                               float delta_error_max,
                               float delta_kp_max,
                               float delta_ki_max,
                               float delta_kd_max,
                               unsigned int mf_type,
                               unsigned int fo_type,
                               unsigned int df_type,
                               int mf_params[],
                               int rule_base[][qf_default],
                               int output_min_value,
                               int output_middle_value,
                               int output_max_value) {
    struct PID* pid = (struct PID*)pika_platform_malloc(sizeof(struct PID));
    pid->kp = kp;
    pid->ki = ki;
    pid->kd = kd;

    pid->delta_kp_max = delta_kp_max;
    pid->delta_ki_max = delta_ki_max;
    pid->delta_kd_max = delta_kd_max;

    pid->delta_kp = 0;
    pid->delta_ki = 0;
    pid->delta_kd = 0;

    pid->error_max = error_max;
    pid->delta_error_max = delta_error_max;

    int output_count = 1;
    if (ki > 1e-4) {
        output_count += 1;
        if (kd > 1e-4)
            output_count += 1;
    }

    pid->fuzzy_struct = fuzzy_init(2, output_count);
    fuzzy_params_init(pid->fuzzy_struct, mf_type, fo_type, df_type, mf_params,
                      rule_base);

    pid->last_error = 0;
    pid->current_error = 0;

    pid->intergral = 0;
    pid->intergral_limit = integral_limit;

    pid->dead_zone = dead_zone;
    pid->feed_forward = feed_forward;

    pid->output_max_value = output_max_value;
    pid->output_middle_value = output_middle_value;
    pid->output_min_value = output_min_value;

    return pid;
}

struct PID* fuzzy_pid_init(float* params,
                           float delta_k,
                           unsigned int mf_type,
                           unsigned int fo_type,
                           unsigned int df_type,
                           int mf_params[],
                           int rule_base[][qf_default]) {
    return raw_fuzzy_pid_init(
        params[0], params[1], params[2], params[3], params[4], params[5],
        max_error, max_delta_error, params[0] / delta_k, params[1] / delta_k,
        params[2] / delta_k, mf_type, fo_type, df_type, mf_params, rule_base,
        min_pwm_output, middle_pwm_output, max_pwm_output);
}

struct PID* raw_pid_init(float kp,
                         float ki,
                         float kd,
                         float integral_limit,
                         float dead_zone,
                         float feed_forward,
                         float linear_adaptive_kp,
                         float error_max,
                         float delta_error_max,
                         int output_min_value,
                         int output_middle_value,
                         int output_max_value) {
    struct PID* pid = (struct PID*)pika_platform_malloc(sizeof(struct PID));
    pid->kp = kp;
    pid->ki = ki;
    pid->kd = kd;

    pid->delta_kp_max = 0;
    pid->delta_ki_max = 0;
    pid->delta_kd_max = 0;

    pid->delta_kp = 0;
    pid->delta_ki = 0;
    pid->delta_kd = 0;

    pid->error_max = error_max;
    pid->delta_error_max = delta_error_max;

    pid->fuzzy_struct = NULL;

    pid->last_error = 0;
    pid->current_error = 0;

    pid->intergral = 0;
    pid->intergral_limit = integral_limit;

    pid->dead_zone = dead_zone;
    pid->feed_forward = feed_forward;

    pid->output_max_value = output_max_value;
    pid->output_middle_value = output_middle_value;
    pid->output_min_value = output_min_value;

    pid->linear_adaptive_kp = linear_adaptive_kp;
    return pid;
}

struct PID* pid_init(float* params) {
    return raw_pid_init(params[0], params[1], params[2], params[3], params[4],
                        params[5], params[6], max_error, max_delta_error,
                        min_pwm_output, middle_pwm_output, max_pwm_output);
}

int round_user(float parameter) {
    if ((int)(parameter * 10.0) % 10 >= 5)
        return parameter + 1;
    else
        return parameter;
}

int limit(int value, int max_limit, int min_limit) {
    if (value > max_limit)
        return max_limit;
    if (value < min_limit)
        return min_limit;
    return value;
}

float fuzzy_pid_control(float real, float idea, struct PID* pid) {
    pid->last_error = pid->current_error;
    pid->current_error = idea - real;
    float delta_error = pid->current_error - pid->last_error;
#ifdef fuzzy_pid_dead_zone
    if (pid->current_error < pid->dead_zone &&
        pid->current_error > -pid->dead_zone) {
        pid->current_error = 0;
    } else {
        if (pid->current_error > pid->dead_zone)
            pid->current_error = pid->current_error - pid->dead_zone;
        else {
            if (pid->current_error < -pid->dead_zone)
                pid->current_error = pid->current_error + pid->dead_zone;
        }
    }
#endif
    fuzzy_control(pid->current_error / pid->error_max * 3.0f,
                  delta_error / pid->delta_error_max * 3.0f, pid->fuzzy_struct);

    pid->delta_kp =
        pid->fuzzy_struct->output[0] / 3.0f * pid->delta_kp_max + pid->kp;

    if (pid->fuzzy_struct->output_num >= 2)
        pid->delta_ki = pid->fuzzy_struct->output[1] / 3.0f * pid->delta_ki_max;
    else
        pid->delta_ki = 0;

    if (pid->fuzzy_struct->output_num >= 3)
        pid->delta_kd = pid->fuzzy_struct->output[2] / 3.0f * pid->delta_kd_max;
    else
        pid->delta_ki = 0;

#ifdef fuzzy_pid_debug_print
    pika_platform_printf("kp : %f, ki : %f, kd : %f\n", kp, ki, kd);
#endif

    pid->intergral += (pid->ki + pid->delta_ki) * pid->current_error;
#ifdef fuzzy_pid_integral_limit
    if (pid->intergral > pid->intergral_limit)
        pid->intergral = pid->intergral_limit;
    else {
        if (pid->intergral < -pid->intergral_limit)
            pid->intergral = -pid->intergral_limit;
    }
#endif
    pid->output =
        (pid->kp + pid->delta_kp) * pid->current_error + pid->intergral +
        (pid->kd + pid->delta_kd) * (pid->current_error - pid->last_error);
    pid->output += pid->feed_forward * (float)idea;
    return pid->output;
}

float pid_control(float real, float idea, struct PID* pid) {
    pid->last_error = pid->current_error;
    pid->current_error = idea - real;

#ifdef pid_dead_zone
    if (pid->current_error < pid->dead_zone &&
        pid->current_error > -pid->dead_zone) {
        pid->current_error = 0;
    } else {
        if (pid->current_error > pid->dead_zone)
            pid->current_error = pid->current_error - pid->dead_zone;
        else {
            if (pid->current_error < -pid->dead_zone)
                pid->current_error = pid->current_error + pid->dead_zone;
        }
    }
#endif

#ifdef pid_debug_print
    pika_platform_printf("kp : %f, ki : %f, kd : %f\n", kp, ki, kd);
#endif

    pid->intergral += (pid->ki) * pid->current_error;
#ifdef pid_integral_limit
    if (pid->intergral > pid->intergral_limit)
        pid->intergral = pid->intergral_limit;
    else {
        if (pid->intergral < -pid->intergral_limit)
            pid->intergral = -pid->intergral_limit;
    }
#endif

    float linear_adaptive_kp = 1;
    if (pid->linear_adaptive_kp > 1e-4)
        linear_adaptive_kp = (1 - pid->linear_adaptive_kp) *
                                 pid->current_error / pid->error_max +
                             pid->linear_adaptive_kp;

    pid->output = pid->kp * linear_adaptive_kp * pid->current_error +
                  pid->intergral +
                  (pid->kd) * (pid->current_error - pid->last_error);
    pid->output += pid->feed_forward * (float)idea;
    return pid->output;
}

void delete_pid(struct PID* pid) {
    if (pid->fuzzy_struct != NULL) {
        delete_fuzzy(pid->fuzzy_struct);
    }
    pika_platform_free(pid);
}

void delete_pid_vector(struct PID** pid_vector, unsigned int count) {
    for (unsigned int i = 0; i < count; ++i) {
        delete_pid(pid_vector[i]);
    }
    pika_platform_free(pid_vector);
}

struct PID** pid_vector_init(float params[][pid_params_count],
                             unsigned int count) {
    struct PID** pid =
        (struct PID**)pika_platform_malloc(sizeof(struct PID*) * count);
    for (unsigned int i = 0; i < count; ++i) {
        pid[i] = pid_init(params[i]);
    }
    return pid;
}

struct PID** fuzzy_pid_vector_init(float params[][pid_params_count],
                                   float delta_k,
                                   unsigned int mf_type,
                                   unsigned int fo_type,
                                   unsigned int df_type,
                                   int* mf_params,
                                   int rule_base[][qf_default],
                                   unsigned int count) {
    struct PID** pid =
        (struct PID**)pika_platform_malloc(sizeof(struct PID*) * count);
    for (unsigned int i = 0; i < count; ++i) {
        pid[i] = fuzzy_pid_init(params[i], delta_k, mf_type, fo_type, df_type,
                                mf_params, rule_base);
    }
    return pid;
}

int direct_control(int zero_value, int offset_value, pika_bool direct) {
    if (direct == pika_true) {
        return zero_value + offset_value;
    } else {
        return zero_value - offset_value;
    }
}

int fuzzy_pid_motor_pwd_output(float real,
                               float idea,
                               pika_bool direct,
                               struct PID* pid) {
    return limit(direct_control(pid->output_middle_value,
                                fuzzy_pid_control(real, idea, pid), direct),
                 pid->output_max_value, pid->output_min_value);
}

int pid_motor_pwd_output(float real,
                         float idea,
                         pika_bool direct,
                         struct PID* pid) {
    return limit(direct_control(pid->output_middle_value,
                                pid_control(real, idea, pid), direct),
                 pid->output_max_value, pid->output_min_value);
}